Hi there! We have alot in common it seems.
I am a student and I'm also making a very similar transition, although from completely the opposite end of the spectrum to you. (the kind of hipstery, art student look)
And to be honest, I think I'm finally starting to succeed, though its been a hard journey.
Build from the bottom up: start with shoes (I'm wearing brogue boots atm) and bottoms (I wear black skinnies but some coloured skinny chinos are on my wish list). Buy loads of plain tops to go with these (no garish huge logos!)
As for the top, keep it simple! Simple colours, simple textures! (don't go straight for cords and tweed yet!) Plain t shirts can be layered with grey or coloured plain knitwear, fairisle and blazers.
As for the money issue, I buy nearly everything from topman or asos. Look in the sale in topman atm, there's some ridiculous buys where I am!
Hope this helps man!